document.write( "Question 775486: what is the distance formula and how would i solve this problem. Find all the points having an x-coordinate of 3 whose distance from the point (-2, -1) is 13. (Hint: The unknown points [there are two of them] have coordinates (3,y), where y is to be determined. Use the coordinates of the given point, the distance, and the distance formula to solve for the required values of y.) \n" ); document.write( "
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Q:
\n" ); document.write( "what is the distance formula and how would i solve this problem. Find all the points having an x-coordinate of 3 whose distance from the point (-2, -1) is 13. (Hint: The unknown points [there are two of them] have coordinates (3,y), where y is to be determined. Use the coordinates of the given point, the distance, and the distance formula to solve for the required values of y.)
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\n" ); document.write( "A:
\n" ); document.write( "The distance between two point (\"x%5B1%5D\", \"y%5B1%5D\") and (\"x%5B2%5D\", \"y%5B2%5D\") is equal to \"sqrt%28%28x%5B2%5D-x%5B1%5D%29%5E2+%2B+%28y%5B2%5D-y%5B1%5D%29%5E2%29\".
\n" ); document.write( "Therefore, the distance between (-2,-1) and (3,y) is
\n" ); document.write( "\"sqrt%28%283-%28-2%29%29%5E2+%2B+%28y-%28-1%29%29%5E2%29\" = 13
\n" ); document.write( "\"sqrt%2825+%2B+%28y%2B1%29%5E2%29\" = 13, square both sides
\n" ); document.write( "\"25+%2B+%28y%2B1%29%5E2\" = 169
\n" ); document.write( "\"%28y%2B1%29%5E2\" = 144, get the square roots of both sides
\n" ); document.write( "y+1 = ±12
\n" ); document.write( "y = -1+12 or y = -1-12
\n" ); document.write( "y = 11 or y = -13
\n" ); document.write( "Answers:The points are (3, 11) and (3, -13)
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